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Book DetailsFields Institute CommunicationsVolume: 25; 2000; 574 ppMSC: Primary 47; 35; 34; 81;
This volume contains a selection of papers presented at an international conference on operator theory and its applications held in Winnipeg. The papers chosen for this volume are intended to illustrate that operator theory is the language of modern analysis and its applications. Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas.
The volume is dedicated to the late A. V. Strauss, whose principal areas of research were spectral theory of linear operators in Hilbert spaces, extension theory for symmetric linear operators, theory of the characteristic functions and functional models of linear operators, and boundary value problems with boundary conditions depending on spectral parameter. The bibliography of publications by A. V. Strauss combined with the papers from the conference provide both historical perspective and contemporary research on the field of operator theory and its applications.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipMathematicians, engineers and graduate students interested in operator theory and its applications, PDEs, ordinary differential equations and quantum theory.

Table of Contents

Chapters

Abraham Strauss — Functional models of regular symmetric operators

A. Ramm — Property C for ODE and applications to inverse problems

Ya. Alber — Decomposition theorems in Banach spaces

Ruben Airapetyan — On a new statement of inverse problem of quantum scattering theory

Ruben Airapetyan, Alexander Ramm and Alexandra Smirnova — Continuous methods for solving nonlinear illposed problems

D. Alpay and Y. Peretz — Quasicoisometric realizations of upper triangular matrices

J. Ball — Linear systems, operator model theory and scattering: Multivariable generalizations

J. Ball and N. Young — Problems on the realization of functions

Sergey Belyi and Eduard Tsekanovskii — Multiplication theorems for $J$contractive operatorvalued functions

Yurij Berezansky — Spectral theory of commutative Jacobi fields: Direct and inverse problems

Giovanni Crosta — The forward propagation method applied to the inverse obstacle problem of electromagnetics

Jan Eisner and Milan Kučera — Spatial patterning in reactiondiffusion systems with nonstandard boundary conditions

Anatolii Ětkin — On an abstract boundary value problem with the eigenvalue parameter in the boundary condition

Fritz Gesztesy and Konstantin Makarov — Some applications of the spectral shift operator

S. Gutman and A. Ramm — Application of the hybrid stochasticdeterministic minimization method to a surface data inverse scattering problem

W. Jäger and P. Rejto — On a theorem of Mochizuki and Uchiyama about long range oscillating potentials I

V. Khatskevich and V. Senderov — Basic properties of linear fractional mappings of operator balls: Schroeder’s equation

Eugene Khruslov and Leonid Pankratov — Homogenization of the Dirichlet variational problems in OrliczSobolev spaces

B. Loginov, D. Rakhimov and N. Sidorov — Development of M. K. Gavurin’s pseudoperturbation method

Julián LópezGómez — A bridge between operator theory and mathematical biology

Marjan Matvejchuk — Measures on effects and on projections in spaces with indefinite metric

Toshitaka Nagai — Concentration behavior of solutions to a chemotaxis system

R. Plato — The solution of linear semidefinite illposed problems by the conjugate residual method

A. Ramm — Justification of the limiting absorption principle in $\mathbb R^2$

A. Ramm — Krein’s method in inverse scattering

Alexander Ramm and Marco Sammartino — Existence and uniqueness of the scattering solutions in the exterior of rough domains

Shigui Ruan and John Clements — Existence and uniqueness of solutions of retarded quasilinear wave equations

Efim Shifrin and Boštjan Brank — On solution of elliptical interface crack problem

Alexander Shklyar — Some new effects for complete second order linear differential equations in Hilbert spaces

Vladilen Trenogin — Abstract boundary value problems for operator equations

A. Tsyganov — On spectral decompositions of a restriction of a differential operator

N. Voitovich, Yu. Topolyuk and O. Reshnyak — Approximation of compactly supported functions with free phase by functions with bounded spectrum

Anatoly Yagola and Konstantin Dorofeev — Sourcewise representation and a Posteriori error estimates for illposed problems

Yoshio Yamada — Coexistence states for LotkaVolterra systems with crossdiffusion

Masaru Yamaguchi and Hiroshi Yoshida — Nonhomogeneous string problem with periodically moving boundaries


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This volume contains a selection of papers presented at an international conference on operator theory and its applications held in Winnipeg. The papers chosen for this volume are intended to illustrate that operator theory is the language of modern analysis and its applications. Together with the papers on the abstract operator theory are many papers on the theory of differential operators, boundary value problems, inverse scattering and other inverse problems, and on applications to biology, chemistry, wave propagation, and many other areas.
The volume is dedicated to the late A. V. Strauss, whose principal areas of research were spectral theory of linear operators in Hilbert spaces, extension theory for symmetric linear operators, theory of the characteristic functions and functional models of linear operators, and boundary value problems with boundary conditions depending on spectral parameter. The bibliography of publications by A. V. Strauss combined with the papers from the conference provide both historical perspective and contemporary research on the field of operator theory and its applications.
Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Mathematicians, engineers and graduate students interested in operator theory and its applications, PDEs, ordinary differential equations and quantum theory.

Chapters

Abraham Strauss — Functional models of regular symmetric operators

A. Ramm — Property C for ODE and applications to inverse problems

Ya. Alber — Decomposition theorems in Banach spaces

Ruben Airapetyan — On a new statement of inverse problem of quantum scattering theory

Ruben Airapetyan, Alexander Ramm and Alexandra Smirnova — Continuous methods for solving nonlinear illposed problems

D. Alpay and Y. Peretz — Quasicoisometric realizations of upper triangular matrices

J. Ball — Linear systems, operator model theory and scattering: Multivariable generalizations

J. Ball and N. Young — Problems on the realization of functions

Sergey Belyi and Eduard Tsekanovskii — Multiplication theorems for $J$contractive operatorvalued functions

Yurij Berezansky — Spectral theory of commutative Jacobi fields: Direct and inverse problems

Giovanni Crosta — The forward propagation method applied to the inverse obstacle problem of electromagnetics

Jan Eisner and Milan Kučera — Spatial patterning in reactiondiffusion systems with nonstandard boundary conditions

Anatolii Ětkin — On an abstract boundary value problem with the eigenvalue parameter in the boundary condition

Fritz Gesztesy and Konstantin Makarov — Some applications of the spectral shift operator

S. Gutman and A. Ramm — Application of the hybrid stochasticdeterministic minimization method to a surface data inverse scattering problem

W. Jäger and P. Rejto — On a theorem of Mochizuki and Uchiyama about long range oscillating potentials I

V. Khatskevich and V. Senderov — Basic properties of linear fractional mappings of operator balls: Schroeder’s equation

Eugene Khruslov and Leonid Pankratov — Homogenization of the Dirichlet variational problems in OrliczSobolev spaces

B. Loginov, D. Rakhimov and N. Sidorov — Development of M. K. Gavurin’s pseudoperturbation method

Julián LópezGómez — A bridge between operator theory and mathematical biology

Marjan Matvejchuk — Measures on effects and on projections in spaces with indefinite metric

Toshitaka Nagai — Concentration behavior of solutions to a chemotaxis system

R. Plato — The solution of linear semidefinite illposed problems by the conjugate residual method

A. Ramm — Justification of the limiting absorption principle in $\mathbb R^2$

A. Ramm — Krein’s method in inverse scattering

Alexander Ramm and Marco Sammartino — Existence and uniqueness of the scattering solutions in the exterior of rough domains

Shigui Ruan and John Clements — Existence and uniqueness of solutions of retarded quasilinear wave equations

Efim Shifrin and Boštjan Brank — On solution of elliptical interface crack problem

Alexander Shklyar — Some new effects for complete second order linear differential equations in Hilbert spaces

Vladilen Trenogin — Abstract boundary value problems for operator equations

A. Tsyganov — On spectral decompositions of a restriction of a differential operator

N. Voitovich, Yu. Topolyuk and O. Reshnyak — Approximation of compactly supported functions with free phase by functions with bounded spectrum

Anatoly Yagola and Konstantin Dorofeev — Sourcewise representation and a Posteriori error estimates for illposed problems

Yoshio Yamada — Coexistence states for LotkaVolterra systems with crossdiffusion

Masaru Yamaguchi and Hiroshi Yoshida — Nonhomogeneous string problem with periodically moving boundaries